On some algorithms for multiple inheritance in object oriented programming

Abstract

We study here some problems yielded by multiple inheritance in object-oriented languages. We give an interpretation and a formalism of heritance mechanisms within the framework of partially ordered sets theory. An inheritance mechanism can be regarded as a traversing algorithm of the inheritance graph, and we prove that those which yields linear extension (total order) play a central role. We discuss some operational semantic aspects of multiple inheritance, with the introduction of a concept named by multiplicity. After a presentation of some well- known inheritance algorithms we propose two new algorithms based upon depth-first search techniques and some particular classes of linear extensions, recently studied. We end by applying these results in the case of inheritance with exceptions and by setting a few problems. All these results are implemented in the frame-based language YAFOOL.